This example uses
webMathematica to model
the spread of an epidemic
throughout a population.

POLYNOMIAL EXPANSION

LONG MULTIPLICATION

DISEASE MODEL

3D PLOT

TORUS KNOTS

 

 

 

Kermack-MacKendrick Disease Model

  Birth Rate (b)

  Infection Rate (v)

  Immunity Rate (c)

The Kermack-MacKendrick model was proposed to explain the rapid rise and fall in the number of infected patients observed in epidemics such as the plague (London 1665-1666, Bombay 1906) and cholera (London 1865). In this model, a total population P is considered to be split into three classes: susceptibles S, those removed due to immunity R, and those currently infected or infectious I. These quantities are then related by the coupled differential equations

where v is the infection rate, b is the birth rate, and c is the immunity rate.

The model assumes:

  1. The population is fixed, so that no one enters, leaves, or dies.
  2. The incubation period is zero.
  3. The duration of infectivity is just as long as the clinical disease.